Louisiana State University LSU Digital Commons LSU Historical Dissertations and Theses Graduate School 1953 Electric Conduction at an Interface. Hung-chi Chang Louisiana State University and Agricultural & Mechanical College Follow this and additional works at: https://digitalcommons.lsu.edu/gradschool_disstheses Part of the Physical Sciences and Mathematics Commons Recommended Citation Chang, Hung-chi, "Electric Conduction at an Interface." (1953). LSU Historical Dissertations and Theses. 8039. https://digitalcommons.lsu.edu/gradschool_disstheses/8039 This Dissertation is brought to you for free and open access by the Graduate School at LSU Digital Commons. It has been accepted for inclusion in LSU Historical Dissertations and Theses by an authorized administrator of LSU Digital Commons. For more information, please contact [email protected]. ELECTRIC CONDUCTION AT AN INTERFACE A Thesis Submitted to the Graduate Faculty of the Louisiana State University and Agricultural and Mechanical College in partial fulfillment of the requirements for the degree of Doctor of Philosophy in The Department of Physics by Hung-Chi Chang B 0 So9 National Chiao-Tung University, Shanghai, China, 1934 Mo So, Louisiana State University, 1951 June, 1953 UMI Number: DP69417 All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. UMI Dissertation Publishing UMI DP69417 Published by ProQuest LLC (2015). Copyright in the Dissertation held by the Author. Microform Edition © ProQuest LLC. All rights reserved. This work is protected against unauthorized copying under Title 17, United States Code ProQuest ProQuest LLC. 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, Ml 48106- 1346 MANUSCRIPT THESES Unpublished theses submitted for the master^ and doctorfs degrees and deposited in the Louisiana State University Library are available for inspection* Use of any thesis is limited by the rights of the author* Bibliographical references may be noted, but passages may not be copied unless the author has given permission* Credit must be given in subsequent "written or published work, A library which borrows this thesis for use by its clientele is expected, to make sure that the borrower is aware of the above restrictions* LOUISIANA STATE UNIVERSITY LIBRARY 119-a ACKNOWLEDGMENT The author is greatly indebted to Professors George Jaffe and Lloyd W. Morris for their encouragement and valuable assistance in this research* He wishes to express his appreciation to U. S. Depart­ ment of State for a grant-in-aid, during the tenure of which most of this work was performed. He also wishes to thank Mr. Charles Roubique and Professor L. W. Morris for the inclusion in this thesis of the curves concerning the selenium rectifier with variable dc bias. \J 4 7 9 8 2 5 TABLE CF CONTENTS PAGE ACKNOWLEDGMENT . * ............................... ii LIST OF TABLES ..................................... v LIST OF FIGURES ..................................... vi ABSTRACT ..................................... viii CHAPTERS I INTRODUCTION ........................ 1 II TRANSFER OF CHARGE THROUGH INTERFACES . 11 1. Crossing process for an ideal interface *•••* 12 2. Exchange process for an ideal interface 15 3. The concept of the general boundary condition ...••••• 16 III GENERAL EQUATIONS FOR THE TIME-INDEPENDENT SPATIAL DISTRIBUTION OF CHARGE CARRIERS, FIELD AND CURRENT AT AN IDEAL INTERFACE . IS 1. Fundamental differential equa­ tions ................... IB 2. Boundary conditions for one polar­ ization layer ...••••••• 22 3* D. C. Solutions *»••»»••» 23 4* A. C. So l u t i o n s ........... 24 IV A. C. CHARACTERISTICS OF AN IDEAL POLARIZA­ TION L A Y E R ..................... 28 1. Characteristics without bias * • • 28 (a) First-order approximation . • 28 (b) Second-order approximation. 35 2. Characteristics with bias. • • • • 40 V THE COMPOUND POLARIZATION LAYER MODEL . 51 1. Compound-interface systems . • • 51 2♦ Two ideal polarization layers in series. * ............... * ........... 55 3. Frequency dependence of l/R and G ...................... P ............58 P VI EXPERIMENTS ON ELECTROLYTIC CONDUCTION .... 61 1. Introduction ............ 61 2. The Continuous Flow Cell 63 3. Electrode forming •«..••••«.• 68 A. The measurements 70 (a) Apparatus and methods •••••• 70 (b) Presentation of data ..••••• 72 VII CORRELATION BETWEEN THEORY AND EXPERIMENT . 75 1* General method 75 2* Preliminary Interpretation............. 81 of data BIBLIOGRAPHY . ............................... 90 APPENDICES A Exact Solutions For A One-species System . 93 B Derivation of N-^(x) For the Case with Bias . 100 C Table of Notation ............. 101 VITA ....................................... 106 LIST OF TABLES Table No, Page I Frequency dependence of the thickness of the polarization layer ( f& as a function of IT ) • • • 39a II Series resistances and capacitances of the aluminum-amnonium borate-aluminum continuous flow cell with variations of molar concentra­ tion, forming voltage, and frequency « . „ (A) Conductance water ...•••.•••••• 72a (B) 0.0001 M ............................. 72b (C) 0.001 M ............................... 72c (D) 0.01 M .............................. 72d III Series resistances and reciprocal series capacitances of the aluminum-aluminum oxide-ammonium borate half cell with variations of molar concentration of am- monium borate, forming voltage and frequency,,. (A) Conductance water ..................... 72e (B) 0.0001 M ............................ 72f (C) 0.001 M ................................ 12g IV Constants throughout all measurements........... 72 V Re suits of matching experimental data on theoretical curves .............. 85 v LIST OF FIGURES Figure No. Page 1 Theoretical curves for the dimensionless parallel conductance 'Yas functions of y and ^ ( j> = <7^y3)......... * • • 33a 2 Theoretical curves for the dimensionless parallel polarization capacitance as functions of 7f and f ( j2 -(Tfh) ........ 33b 3 Theoretical curves for the dimensionless parallel conductance % . ( A r , o ) as functions of ft and X considering the thickness of the polarization layer to be constant • ............... * 38a 4 Theoretical curves for the dimensionless parallel polarization capacitance as functions of ft and X con­ sidering the thickness of the polarization layer to be c o n s t a n t ....................... 38b 5 Experimental curves for l/R of selenium recti­ fiers at 60 cps with variatEons of bias and forming * ........................... • • . • 47a 6. Experimental curves for CO C of selenium recti­ fiers at 60 cps with variations of bias and forming (curves A, B, C) ............. 47b 7 Experimental curves for CO C of selenium rectifiers at 60 cps with variations of bias and forming (Curves D, E, F) . .......... * 47c (Figs, 5, 6 and 7 are reproduced respectively from Figs. IV G, H and I. Final Report on the Dry Disc Rectifier contract for the Signal Corps Project No* 152 B) S Correction curves of the dimensionless parallel con­ ductance for the addition of an insulation layer at the interface • • • # 58a 9 Correction curves of the dimensionless parallel capacitance for the addition of an insulation layer at the interface ......... 58b 10 Cross section diagram of continuous flow cell . * 64a 11 Diagram of bridge assembly 70a vi Figure No. 12 Series capacitance of aluminum-aluminum oxide-water half cell with variation of forming voltage ... ....•••• 73a 13 Series capacitance of aluminum-aluminum oxide ammonium borate half cell with variations of forming voltage. 0.0001 M ......... 73b 14- Series capacitance of aluminum-aluminum oxide ammonium borate half cell with variation of forming voltage. 0*001 M ......... ........ 73c 15 Series resistances of the aluminum-aluminum oxide-ammonium borate half cell with variations of concentration and forming voltage. ........ 73d. 16 Dimensionless normal resistance and reciprocal geometrical capacitance 76a 17 Effect of insulation layers of variable cap­ acitances upon the normal l/C curve. * 78a 18 Combination of two normal R curves showing the cross over phenomenon 78b 19 Dependence of of the polarization layer on frequency and forming voltage .................. • 82a 20 Dependence of l/Rp of the polarization layer on frequency and forming v o l t a g e .......... 82b vii ABSTRACT In an attempt to provide a basis for the investigation of electric conduction through metal-semiconductor and metal-solution interfaces, the author gives a microscopic interpretation of the general boundary condition, previously formulated, and introduces the concept of ideal and compound interfaces* The electric potential difference across an ideal interface can be assumed to be zero and therefore the charge trans­ fer rate for an ideal interface is independent of the applied voltage* Any actual interface may be considered as a compound interface and can be represented by a combination of several ideal interfaces* With this general boundary condition, the universal functions of the parallel conductance l/R and parallel capacitance C for an ideal P P polarization layer in an n-species system are calculated to the second- order approximation for the ac case without dc bias. The value of the first- order 0^ is modified appreciably and the second-order indicates the existence of a maximum capacitance occurring